A Fourier-Bessel Test of the Gravitational Inverse-Square Law

Abstract

This dissertation presents the latest E\"{o}t-Wash group test of the gravitiational Inverse Square Law (ISL) at the shortest possible distances using a stationary torsion pendulum above a rotating attractor. It largely builds off of earlier Fourier-Bessel work of Ted Cook \cite{cook2013test} that utilized test-masses with both 18-fold and 120-fold azimuthal symmetries. In this case, the effective masses of the platinum test bodies of the 18- and 120-fold patterns on the pendulum were 0.21 and 0.62 mg. We tested the ISL at separations ranging from 52$\mu$m to 3mm. We have excluded at 95\% confidence gravitational strength Yukawa interactions with length scales $\lambda > 39\mu$m and set new limits between $\lambda = 8\mu$m and $90\mu$m. We have resolved gravitational interactions at the closest separations ever and measured a new systematic arising from the magnetic susceptibilities of our test-mass materials. We present a full description of the instrument, the analysis methods, and the results.